An alternative proof of Theorem REF  using Niemeier lattices was later given by Hashimoto [1]}. The lattices themselves have been exhibited by
Morrison [2]} and Van Geemen-Sarti [3]} for \(p=2\)  and by Garbagnati-Sarti [4]} for the odd primes in a case-by-case manner (they denote the lattice \(\mathbf {L}_p\)  by \(\Omega _p\) ).
